Simplify (7-21x)/6*(4x+10)/(14-42x)

$\frac{7 - 21 x}{6} \cdot \frac{4 x + 10}{14 - 42 x}$

Step 1

Factor $7$ out of $7 - 21 x$ .

Factor $7$ out of $7$ .

$\frac{7 (1) - 21 x}{6} \cdot \frac{4 x + 10}{14 - 42 x}$

Factor $7$ out of $- 21 x$ .

$\frac{7 (1) + 7 (- 3 x)}{6} \cdot \frac{4 x + 10}{14 - 42 x}$

Factor $7$ out of $7 (1) + 7 (- 3 x)$ .

$\frac{7 (1 - 3 x)}{6} \cdot \frac{4 x + 10}{14 - 42 x}$

Step 2

Factor $2$ out of $4 x + 10$ .

Factor $2$ out of $4 x$ .

$\frac{7 (1 - 3 x)}{6} \cdot \frac{2 (2 x) + 10}{14 - 42 x}$

Factor $2$ out of $10$ .

$\frac{7 (1 - 3 x)}{6} \cdot \frac{2 (2 x) + 2 (5)}{14 - 42 x}$

Factor $2$ out of $2 (2 x) + 2 (5)$ .

$\frac{7 (1 - 3 x)}{6} \cdot \frac{2 (2 x + 5)}{14 - 42 x}$

Step 3

Factor $14$ out of $14 - 42 x$ .

Factor $14$ out of $14$ .

$\frac{7 (1 - 3 x)}{6} \cdot \frac{2 (2 x + 5)}{14 (1) - 42 x}$

Factor $14$ out of $- 42 x$ .

$\frac{7 (1 - 3 x)}{6} \cdot \frac{2 (2 x + 5)}{14 (1) + 14 (- 3 x)}$

Factor $14$ out of $14 (1) + 14 (- 3 x)$ .

$\frac{7 (1 - 3 x)}{6} \cdot \frac{2 (2 x + 5)}{14 (1 - 3 x)}$

Step 4

Cancel the common factor of $7 (1 - 3 x)$ .

Factor $7 (1 - 3 x)$ out of $14 (1 - 3 x)$ .

$\frac{7 (1 - 3 x)}{6} \cdot \frac{2 (2 x + 5)}{7 (1 - 3 x) (2)}$

Cancel the common factor.

$\frac{7 (1 - 3 x)}{6} \cdot \frac{2 (2 x + 5)}{7 (1 - 3 x) \cdot 2}$

Rewrite the expression.

$\frac{1}{6} \cdot \frac{2 (2 x + 5)}{2}$

Step 5

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{1}{2 (3)} \cdot \frac{2 (2 x + 5)}{2}$

Cancel the common factor.

$\frac{1}{2 \cdot 3} \cdot \frac{2 (2 x + 5)}{2}$

Rewrite the expression.

$\frac{1}{3} \cdot \frac{2 x + 5}{2}$

Step 6

Multiply $\frac{1}{3}$ by $\frac{2 x + 5}{2}$ .

$\frac{2 x + 5}{3 \cdot 2}$

Step 7

Multiply $3$ by $2$ .

$\frac{2 x + 5}{6}$

Simplify (7-21x)/6*(4x+10)/(14-42x)

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